(a) The function describes a parabola that opens downward. The value of A(x) is zero when x=0 and when x=100. The vertex (maximum) is halfway between those zeros, at x=50. The dimensions are 50 and 100-50 = 50. The maximum area pen will be 50 ft square.
(b) A(50) = (50 ft)² = 2500 ft² . . . the maximum area
(c) A(x) will be negative if x < 0 or x > 100, so the domain is 0 ≤ x ≤ 100.
The value of A(x) ranges from 0 to its maximum, 2500. Hence the range is 0 ≤ A(x) ≤ 2500.
For a rectangular fenced area, the dimensions that maximize the area are 50 feet by 50 feet, given a total of 200 feet of fence. The maximum possible area is 2500 square feet. The domain for this function is [0, 100] and the range is [0, 2500].
Explanation:This problem deals with maximizing an area given a certain length of fencing. It is a part of optimization problems often encountered in calculus. Firstly, we understand that a rectangle will give maximum area for a fixed perimeter. Considering a rectangle, the dimensions would be x and 100-x, where x is one of the sides of the rectangle.
(a) To find the dimension that maximizes the area, we first need to find the derivative A'(x) of A(x), which equals to -2x + 100. Setting A'(x) to zero gives us x = 50. That means the dimensions that will give us maximum area are 50 feet by 50 feet.
(b) Substituting x = 50 back into the original function, we find that the maximum area is A(50)=50(100-50)=50*50=2500 square feet.
(c) For the domain of A in this application, it would be all possible values of x. So, x could be any number from 0 to 100 (both inclusive). The range of A would be from 0 to the maximum value, 2500 square feet.
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is the square root of 10 greater than,less than or equal to 5
CD player: $120, 20% markup (show work)
collection of dimes and quarters has a total of $19.55. If there are three times as many quarters as dimes, find the number of each?
During a certain week, a post office sold Rs.280 worth of 14-paisas stamps. How many of these stamps did they sell?
The post office sold 2000.
To find out how many 14-paisa stamps the post office sold to make Rs.280, we need to follow a step-by-step solution.
Convert the total amount from rupees to paisas:Since the stamp's value is given in paisas.There are 100 paisas in 1 rupee.Rs.280 = 280 x 100 = 28000 paisas.The value of one stamp is 14 paisas.To find the number of stamps sold, we divide the total amount in paisas by the value of one stamp:28000 paisas ÷ 14 paisas per stamp = 2000 stamps.
Lilia parked her 18 model cars in equal rows. 3time6. Write another way lilia could arrange her cars in equal rows
At a store, hot dogs come in packages of eight and hot dog buns come in packages of twelve. What is the least number of packages of each type that you can buy and have no hot dogs or buns left over?
liam is setting up folding chairs for a meeting. if he arranges the chairs in 9 rows of the same length, he has 3 chairs left over. if he arranges the chairs in 7 rows of the same length, he hass 19 left over. How many chairs does Liam Have
five quarts of latex enamel paint will cover about 100 square feet of wall surface. how many quart are needed to cover 71 square feet of kitchen wall and 69 square feet of bathroom wall ?
A deep-sea diver is in search of coral reefs. He finds a beautiful one at an elevation of -120 4/7 feet. While taking pictures of the reef, he catches sight of a manta ray. He swims up 25 3/7 feet to check it out. What is the diver's new elevation?
The position of the diver's new elevation will be negative 666 / 7.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A remote ocean jumper is looking for coral reefs. He tracks down a wonderful one at a rise of - 120 ⁴/₇ feet. While taking photos of the reef, he sees a manta beam. He swims up 25 ³/₇ feet to look at it.
Convert the mixed fraction number into a fraction number. Then we have
- 120 ⁴/₇ = - 844 / 7
25 ³/₇ = 178 / 7
The position of the diver's new elevation will be given as,
⇒ - 844 / 7 + 178 / 7
⇒ (- 844 + 178) / 7
⇒ - 666/7
The position of the diver's new elevation will be negative 666 / 7.
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how do i find 3/4 of 460
Can I get some points? Please ask me a very simple question like 1 plus 1 or sum and I will answer and get pts? please? Youll get 10 points lol if you have a lot can I get like 70 or sum
Answer:the answer is two double check i could be wrong
Step-by-step explanation:1 x 1 x 1 + 1 / 1 = 2
99 POINTS TOP RECORD I NEED PRO'S FOR THIS!
HELP ASAP
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(-10.3)(2)x = 4(-10.3)(2)
cross out the same terms on both sides and you end up with x =4
which decimal represents the fraction of candles in this group that have flames
A farmer harvested 35 acres of corn and 20 acres of beans. Animals ate 1/8 of the corn he originally planted. how many acres of corn did the farmer plant?
A really bad carton of 18 eggs contains 9 spoiled eggs. an unsuspecting chef picks 6 eggs at random for his "mega-omelet surprise." find the probability that the number of unspoiled eggs among the 6 selected is
Final answer:
To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population.
Explanation:
To find the probability that the number of unspoiled eggs among the 6 selected is X, we can use the hypergeometric probability formula. This formula is used when the sample drawn is without replacement from a finite population. In this case, we have 18 total eggs in the carton, with 9 spoiled eggs. So the probability that X unspoiled eggs are selected out of the 6 can be calculated as:
P(X) = (C(X,6) * C(9,6)) / C(18,6)
Where C(n,r) represents the combination of n things taken r at a time.
Is this a direct variation? 4y=x
The equation 4y = x represents a direct variation. This type of relationship between variables implies that the ratio between x and y is constant. In this specific example, the constant of variation is 0.25.
Explanation:Yes, the given equation 4y = x is a representation of direct variation. Direct variation in mathematics refers to a situation where the ratio of two variables is constant. In a direct variation equation the form is y = kx, where k is the constant of variation. Here, you can rewrite 4y = x as y = x/4 or y = 0.25x, so the constant of variation is 0.25. It's important to note that a direct variation has no y-intercept, it always passes through the origin (0,0) which is the case in this equation.
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first person to get this right gets brainliest how old is obama
Solve each equation 4y-x=16
Which best describes angelica solution
The error that Angelica made is an error substituting the values into the Pythagorean theorem. The equation should be c² + 6² = 10²
How to use Pythagoras Theorem?
From the brainly link attached below, we can see the steps Angelica used in calculating the distance between the two points shown on the graph below.
The steps she took are;
Step 1: Use the point C(–4, –5) to make a right triangle with the 90 degree vertex at C.
Step 2: Determine the lengths of the legs: AC = 6 and BC = 10.
Step 3: Substitute the values into the Pythagorean theorem: 10² = 6² + c²
Step 4: Evaluate
From the graph and looking at the steps she took, we can say that the error that Angelica made is an error substituting the values into the Pythagorean theorem. The equation should be c² + 6² = 10²
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Graph the following sequence of transformations for
jose rodriguez's checking account had a starting balance of 1,234.56. he wrote a check for 115.12 for plumbing supplies and check for 225.00 for a loan payment. Yesterday he deposited 96.75 in his checking account. what jose's current balance?
Please help me with this
zero would be where the slanted line crosses the x axis, in tis picture that would be -6
so answer is A
A single microvillus is a rod-like structure that is 1.0 μm in height. it has a hemispherical top approximately 0.1 μm in diameter. calculate the surface area of the cylinder that forms the "sides" of the microvillus rod. use 3.14 for π.
Final answer:
The surface area of the cylinder forming the sides of a microvillus rod with a diameter of 0.1 µm and a height of 1.0 µm is 0.314 µm².
Explanation:
To calculate the surface area of the cylinder that forms the "sides" of the microvillus rod, we will use the formula for the surface area of a cylinder without the top or bottom, which is circumference multiplied by height
(A = 2πrh).
Since the diameter (d) of the microvillus is given as 0.1 µm, we first find the radius (r) by dividing the diameter by 2.
Therefore, r = 0.1 µm / 2 = 0.05 µm.
The height (h) is given as 1.0 µm.
Inserting these values into our formula, we get:
A = 2 × 3.14 × 0.05 µm × 1.0 µm = 0.314 µm².
Hence, the surface area of the sides of the microvillus rod is 0.314 µm².
Matty jogs 9 km/hr. Identify the correct conversion factor setup required to compute Matty's speed in m/s.
Answer:
2.5 m/s
Step-by-step explanation:
we have given that Matty jogs 9 km/hr
we have to convert 9 km/hr to m/s
we know, 1 km= 1000 m
and 1 hr= 60 minutes and 1 minute= 60 seconds
which implies that 1 hr=60 x 60 = 3600 seconds
now, to convert km/hr into minute/second we have to multiply it by 1000/3600 or 5/18
i.e. 9×1000/3600= 5/2=2.5 m/s
i need help due tommorrow !
9/11÷13/33
what step can you take to check that your results is correct
A. multiply your results by 13/33
B. multiply your results by11/9
C. multiply your results by 9/11
D. multiply your results by 13/33
From 1980 to 1990, Lior’s weight increased by 25%. If his weight was k kilograms in 1990, what was it in 1980?
Ththe weight of Lior in 1990 in terms of k is [tex]\frac{4}{5} k[/tex]
Let the weight of Lior in 1980 be "w"
If Lior's weight increased by 25%, his new weight was "k". This can be expressed as:
w + (25% of w) = k
w + (0.255w) = k
w + 0.15w = k
1.25w = k
Divide both sides by 1.25
[tex]\frac{1.25w}{1.25} =\frac{k}{1.25} \\w=\frac{k}{1.25} \\w=\frac{100k}{125} \\w=\frac{4}{5}k[/tex]
This shows that the weight of Lior in 1990 in terms of k is [tex]\frac{4}{5} k[/tex]
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Another order calls for 26 widgets. The widgets comes in boxes of 5. How many full boxes of 5 do you pull? How many single items do you still need?
divide 26 by 5
26 /5 = 5.2
so 5 full boxes
5*5 = 25
26-25 = 1
so 5 full boxes and 1 single widget
For an order of 26 widgets with each box containing 5 widgets, you would pull 5 full boxes and still need 1 more single widget.
Explanation:To solve this problem, we need to find out how many full boxes of 5 widgets we can make from 26 widgets and how many single widgets we will have left. Whole number quantities, such as the number of widgets and boxes, are important here. First, we divide 26 by 5 to find out the number of full boxes. This gives us 5 full boxes with a remainder of 1, which means we have one widget left. So, we pull 5 full boxes and still need 1 more single widget.
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What is the ordered pair for point K? A. (–4,–5)
B. (4,–5)
C. (5,–4)
D. (–4,5)
Answer:
B
if you read the graph it is 4,-5
What is the distance between the center of the circle with equation x^2+y^2=2x+4y-1 and the point (13,7)?
simplify the expression 4y - 1 - 3y + 2